Recall the coffee robot from the introduction to the previous chapter (page 355). This robot is programmed to move among cafés, order coffee, and record the waiting time. The previous chapter focused on the fact that the robot learns more efficiently when it pools information among the cafés. Varying intercepts are a mechanism for achieving that pooling.
Now suppose that the robot also records the time of day. The average wait time in the morning tends to be longer than the average wait time in the afternoon. This is because cafés are busier in the morning. But just like cafés vary in their average wait times, they also vary in their differences between morning and afternoon. In conventional regression, these differences ...
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